New Kdice Luck Stats - Attn: Math geeks

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New Kdice Luck Stats - Attn: Math geeks

As far as I can tell the luck stat is a simple one sided calculation that works like this: (roll / potential roll)*100 = Luck % ...
I don't know for sure if that's how it is calced, but I bet it is pretty close to that.
So let's look at this example: You roll a 3 v 4 and win. In this situation you rolled a 8 and the other guy rolled 7... Happens all the time. According to the luck stat, your luck is now 44%. But you just one a 3v4! And your luck is mathematically less then 50%! Something isn't right!

In that situation, the 4 dice holds an 80.8% advantage over the 3, but in this example the three won, but his luck stat shows his luck is less then 50%... You just got lucky, and the math doesn't reflect it...

So what I'd like to do, is offer Ryan a new algorithm for calculating luck. Something that takes into account both players rolls... Not just potential rolls...

I've been working on it, but haven't come up with a good one yet, so I am looking for feedback...

If you've never written these types of calculations, here's what I'm looking for specifically-

1. The Algorithm should take into account probability of a successful engagement

2. The algorithm should have no more then 4 variables (2 is ideal: Note - the fewer the variables taken into consideration, the lighter the server load)

3. The algorithm should have a scalable attribute to it (per roll, per game, per per month, per career)

There is a resource table of win/lose probabilities located at the bottom of: http://kdice.wikispaces.com/

I look forward to seeing what you folks come up with, even if it doesn't get deployed, it is a nice mental exercise...

Sincerely,
Wind

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Personally I think it would better to keep it simple and transparent, so at least people can understand what the number means.

I don't think there's any easy way to make a "perfect" luck algorithm--initial territory and dice placement, start order, and restacks are also big "luck" factors and there's no easy way to quantify them (though I'm sure some network theory geek could come up with something).

IMO a simple and transparent algorithm is better than a marginally "better" but less understandable one.

Your idea also clouds the stat itself--now it's not just your luck, it's also a mix of the luck of the people you engaged with. One could argue that someone else being particularly unlucky against you shouldn't translate to you being lucky.

well to be honest while there might be the lucky rolls like the one you stated, that is just one dice roll, think about it for a second, every game you play you have dozens of attacks and defenses which help to even the luck out. also the chance of winning an even battle (same number of dice on both sides) is just under 50% so a persons luck to be 'neutral' should be under 50% (i think someone said 48.4%)

Combined with the fact i believe that the luck stats in the profile only update after a game has been finished, i believe that the person in question had just been unlucky before that roll so their luck was lower than it would of been after the update

I've always thought that it should just show your average individual die roll on offense and defense rather than a luck %. I would understand that better. If it showed that on average you are rolling a 2.3 then your luck sucks, if you are rolling a 4.1 then your luck is great.

Windwalker

According to Ryan in his January blog, the luck stat is based on a table and is calculated for each roll. The table is two-dimensional, so there are three inputs: attacker dice, defender di(c)e, and outcome. So your three points are taken care of in the luck stat.

The luck is the combination of two numbers, one based on your probability of winning the roll and the other based on your probability of losing. I don't remember the exact formula.

This is a hard problem.

The trick is that luck is not really just whether you get your fair share of 6's but when you get em.

6's in round 1 are more useful than round 5.
6's in a 4v4 are more useful than in an 8v2.
6's are more useful when you are losing the game then when you are winning.
6's are more useful when you are connecting then when you aren't.
6's are more useful when your opponent just rolled a bunch of 6's.
6's are more useful when you are playing good opponents than bad ones.
6's are more useful at higher point tables than lower ones.

etc.

There is one possible shortcut to interpreting when the rolls matter, and that's to have the players indicate when they matter. You'd have to do that by giving some manner of 'extra luck' button that adds an extra +1 or something to your next roll after you click it (of which there would be limited use). You would then do an analysis on these particular rolls (treating them as equal importance). This has a lot of failings and is pseudo-scientific, but I think in practice would get you closer than any alternative.

how about something along the lines
if you won:
0.5 + (chanse of win)/2
and if you lost:
0.5 - (chanse of loss)/2

this will give if you forex win 3 times with 80.8% and loose one time with 50%

(((0.50 + (0.19 / 2)) * 3) + 0.25) / 4 = 0.508750

50.9 % luck, and if you look at it chanse for winning 3 rolls at 80.9%
0.809 * 0.809 * 0.809 = 0.529475129

this way the average luck will alwawys be 50 %

Not bad Kreuz, i'd like this one more then the stupid ((roll/6)*100)% calculation (is that what it looks like currently Ryan?). But I still dont like the aspect, that if you have say 70% luck in early game, and then start crushing others with many 8v2 and similar, your luck will go down towards 50%.

the server method should look something like this in java

double odds (int a, int d, boolean r){
if(r){
return 0.5 +oddstable[a][d]/2.0;
}else{
return 0.5 - (1.0-oddstable[a][d])/2.0;
}
}

where a =#attacking dice
d = # defending dice
r = true if attacker win and false if he lost
and the array oddstable is a doublearray with the winninpercentage for attacking v defending dice. i am sure all of theese variables exists in the server already, and you could program this in any language, altho i choose java here, since i bet that is what ryan uses

For the real stat geeks, it would be really cool to have a Win Probability chart like they do in baseball - see http://www.fangraphs.com/wins.aspx?date=2008-10-27&team=Phillies&dh=0&season=2008

Just to plot out the chance at 1st for each player. The main problem being that I have absolutely no idea how you could chart this # except for by taking into account number of connected dice and number of total dice at the start of each turn and compare it with the relative positions of all the other players on the table. It would be interesting in this type of chart to see the impact of a lost 8v8 or a 8v5 defend or something like that.

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